Related papers: Extracting joint weak values from two-dimensional …
The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…
A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…
We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body Schroedinger operators, this leads to a limiting absorption principle that is uniform on the…
For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient…
A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a…
Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a…
This paper considers the problem of detecting a few signals in high-dimensional complex-valued Gaussian data satisfying Johnstone's (2001) \textit{spiked covariance model}. We focus on the difficult case where signals are weak in the sense…
Recently there has been an interest in applying the concept of weak values and weak measurements to condensed matter systems. Here a weak measurement protocol is proposed for obtaining the $Z_2$ index of a topological insulator. The setup…
A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital…
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…
Weak values of quantum observables are a powerful tool for investigating quantum phenomena. Some methods for measuring weak values in the laboratory require weak interactions and postselection, while others are deterministic, but require…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the…
We study the existence of negative eigenvalues for two-dimensional Schr\"odinger operators with real-valued potentials in the weak coupling regime. In his pioneering paper [Simon 1976] from half a century ago, Simon was the first to…
Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a…
The extraordinary concept of weak value amplification has attracted considerable attention for addressing foundational questions in quantum mechanics and for metrological applications in high precision measurement of small physical…